Survival probability in one dimension for theA+B→B reaction with hard-core repulsion

We study the effect of hard-core repulsion (known as the bus effect) betweenB particles on the reaction-diffusion systemA+BB in the continuous-time random walk model in one dimension with theA particles stationary. We show rigorously that the survival probability of theA particles is asymptotically bounded asC ₁lim _t{[–logS(t)]/t ^0.5}C ₂, whereC ₁ andC ₂ are constants. We also do simulations to confirm our results.     

Optimum oxide thickness for dye-sensitized solar cells—effect of porosity and porous size. A numerical approach

The microstructure of the metal semiconductor oxide which forms the heart of a dye-sensitized solar cell (DSSC) has proved to play a key role in the enhancement of photoelectric conversion efficiency of the cell. In this work, a numerical simulation of the system TiO₂ photo-sensitive dye of a TiO₂ DSSC focuses on the effect that the oxide porosity and the size of the pores have on the cell's performance. The steady-state numerical model used is based on the continuity and transport equations for charge species involved in the system, in connection to Poisson's equation. Light absorption coefficient is set dependent on both porosity and the size of pores in TiO₂. At a first approximation, electron mobility is considered dependent upon porosity following an iteration procedure dependent also upon local field in the oxide. An effective dielectric constant dependent upon the porosity of TiO₂, as well, is used in the model. Electron lifetime in the bulk is set dependent upon electron distribution following the iteration procedure with electron lifetime at the surface taking into consideration surface recombination. Results for different values of TiO₂ porosity and pores' size in connection to the oxide thickness are discussed and found in accordance with results reported in the literature.     

Electronic transport in LCMO/BTO composites

A series of (1 ? x)La_0.67Ca_0.33MnO₃/(x)BaTiO₃ composites has been synthesized by the solid state route. Microstructural and transport studies on these samples show a complete immiscibility between metallic ferromagnet, La_0.67Ca_0.33MnO₃ (LCMO) and insulating ferroelectric, BaTiO₃ (BTO). Temperature dependent electrical transport studies show evidence of both intrinsic and extrinsic colossal magnetoresistance (CMR) effects. Inclusion of BTO in LCMO phase results in high resistive samples with a metal-insulator transition at temperature T_{p 1} originating from intrinsic effect and another dominant metal-insulator transition at temperature T_{p 2} caused because of extrinsic effect. T_{p 2} decreases up to a certain percentage of BTO content above which this trend of variation is reversed.     

In-situ and ex-situ study of crystallization behaviour of magnetron sputtered Ni63Zr37 amorphous thin film

ABSTRACT

The stages of crystallization of magnetron sputter-deposited Ni₆₃Zr₃₇ film with mostly amorphous structure have been investigated by differential scanning calorimetry (DSC) and in-situ annealing at 300°C by use of heating stage on a high-resolution transmission electron microscope (HRTEM). These results have been further confirmed by grazing incidence X-ray diffraction analyses of thin film specimens annealed ex-situ at 300°C for various durations. The temperature for crystallization found by DSC has been found to increase from 371°C to 434°C with an increase in heating rate from 3°C/min to 10°C/min, and the apparent activation energy for amorphous to crystalline transformation has been found as ～260.2?kJ/mol from the Kissinger plot. Studies on HRTEM using in-situ heating stage have shown the crystallization to occur on annealing at 300°C for ～10?min. Crystallization at a temperature lower than that found by DSC is attributed to structural relaxation with reduction of free volume due to thermal activation. It has been observed that Ni₃Zr forms first due to its large negative enthalpy of formation, and is followed by the formation of Ni-rich solid solution (Ni_ss) grains. HRTEM studies have shown grain rotation with the formation of partial dislocations at Ni₃Zr-Ni_ss interfaces as well as twinning followed by detwinning with dislocation formation in the Ni_ss matrix possibly to reduce the interfacial energy.     

On an Archimedean analogue of Tate's conjecture

We consider an Archimedean analogue of Tate's conjecture, and verify the conjecture in the examples of isospectral Riemann surfaces constructed by Vignéras and Sunada. We prove a simple lemma in group theory which lies at the heart of T. Sunada's theorem about isospectral manifolds.     

On a Markoff-like chain

Set {I_r = θ|θ = [a₀, a₁, a₂, …, a_n, …] with a_n ≥ r from some point on}. In the context of I₁ (the set of all irrational numbers) the chain of approximation theorems is the well-known Markoff chain (J. W. S. Cassels, “An Introduction to Diophantine Approximation,” Cambridge Tracts No. 45, Cambridge, 1959). The purpose of this paper is to find the chain of approximation theorems when restricted to I_r with r ≥ 2.     

EPR and optical absorption studies on VO ions in KZnClSO4·3H2O single crystals—an observation of superhyperfine structure

EPR spectra of VO²⁺ ions doped in KZnClSO₄·3H₂O single crystals have been studied at different temperatures. The EPR spectrum shows a well-resolved hyperfine and superhyperfine structure patterns. The angular variation of EPR spectra reveals the presence of more than three magnetic complexes, which correspond to distinct sites of VO²⁺ ion. From the angular variation EPR data, the spin-Hamiltonian parameters are evaluated and discussed. The optical absorption spectrum studied at room temperature shows bands corresponding to C_4v symmetry. From the EPR and optical data, the molecular-orbital bonding coefficient ε² and β² are evaluated and discussed. The observed five-line superhyperfine structure has been attributed to four protons (with I=1/2) from the surrounding water molecules of one of the vanadyl sites.     

On the minimum degree,edge-connectivity and connectivity of power graphs of finite groups

In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently, the minimum disconnecting sets of power graphs of the aforementioned groups are determined. In order to investigate the equality of connectivity and minimum degree of power graphs, certain necessary conditions for finite groups and a necessary and su?cient condition for finite cyclic groups are obtained. Moreover, the equality is discussed for the power graphs of abelian p-groups, dihedral groups and dicyclic groups.     

Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups

Young’s orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups, just like the chain of symmetric groups, has multiplicity-free restrictions for irreducible representations. Therefore each irreducible representation of an alternating group also admits Gelfand-Tsetlin bases. Moreover, each such representation is either the restriction of, or a subrepresentation of, the restriction of an irreducible representation of a symmetric group. In this article, we describe a recursive algorithm to write down the expansion of each Gelfand-Tsetlin basis vector for an irreducible representation of an alternating group in terms of Young’s orthogonal basis of the ambient representation of the symmetric group. This algorithm is implemented with the Sage Mathematical Software.     

Pump spectral linewidth influence on stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) and self‐termination behavior of SRS in liquids

The threshold, temporal behavior, and conversion efficiency of stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SBS) in three liquids (benzene, hexane, and dimethyl sulfoxide) and two crystals (calcite and barium nitrate) have been investigated under three largely different spectral linewidth conditions. Pumped with 532‐nm and nanosecond duration laser pulses of ≤ 0.01 cm^?1 linewidth, only SBS can be generated in all tested liquids with a high nonlinear reflectivity. However when the pump spectral linewidth is ～0.07 cm^?1 or ～0.8 cm^?1, both SBS and SRS can be observed in benzene while only SRS can be generated in dimethyl sulfoxide; in all these cases SRS is the dominant contribution to the stimulated scattering but the efficiency values are drastically decreased due to the self‐termination behavior of SRS in liquids, which arises from the thermal self‐defocusing of both pump beam and SRS beam owing to Stokes‐shift related opto‐heating effect. In contrast, for SRS process in the two crystals, the thermal self‐defocusing influence is negligible benefitting from their much greater thermal conductivity, and a higher conversion efficiency of SRS generation can be retained under all three pump conditions.